Question

A) P(Z <-1.26) b) P(Z > 1.48) c) P(1.44 < Z<2.79)

Answer 1

Answer:

• a) P (Z < - 1.26) = 0.60383

• b) P (Z > 1.48) = 0.56944

• c) P (1.44 < Z < 2.79) = 0.07229

Explanation:

You need to use a table with the cumulative normal standard distribution, which shows the areas for different values of Z-scores.

I attached part of the table for the cumulative probability that  gives the probability that a statistic is between 0 (the mean) and Z.

a) P (Z < - 1.26)

The table shows the probabilities for positive values of Z. Since the normal distribution is symmetric P (Z < - 1.26) = P (Z > 1.26).

Also, note that you will find the probability for Z ≤ 1.26, so the probability that you want is P (Z > 1.26) = 1 - P(Z ≤ 1.26)

• From the table: P (Z ≤ 1.26) is 0.39617.

• Then, P (Z > 1.26) = 1 - 0.39617 = 0.60383.

• As said, P (Z < - 1.26) = P (Z > 1.26), so it is 0.60383.

b) P (Z > 1.48)

• P (Z > 1.48) = 1 - P( Z ≤ 1.48)

• From the table, P (Z < 1.48) = 0.43056

• P (Z > 1.48) = 1 - 0.43056 = 0.56944

c) P (1.44 < Z < 2.79)

• P (1.44 < Z < 2.79) = P (Z < 2.79) - P (Z < 1.44)

• From the table: P (Z < 2.79) = 0.49736, and P (Z < 1.44) = 0.42507

• P (Z < 2.79) - P( Z < 1.44) = 0.49736 - 0.42507 = 0.07229